7. How many points of intersection exist between y= x+ 4x2 - 2x-5 and y = 3? %3D A None One Two D Three Four E.

Q: Find the general solution of x(x + 3)dy = 2dy + √(9- y²)(12x + 9 + 4x²) dx.

A: We will separate variables and then will integrate it to find general solution of given differential…

Q: 2. Use separation of variables to solve the following equations: (a) (y² + 1)dy + (e² + x)dx = 0.

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Q: Find the solution of dy e y- dr ey +e-2x-y

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Q: The particular solution of y+y-2y = e?x is

A: To find The particular solution of the given D.E.

Q: Is y = e-x + 2xe-* a solution to y" + 2y' + y = 0.

A:

Q: d'x +x=f(t), if x =x' = 0 for t = 0. Solve d?

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Q: S¹₁₁ S1+₂x² x + 2y dy dx ·12x²

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Q: 1.Solve the given problem W = f(x, y, z) = 3x²y+ yz² + 2z³ fxis equal to ? fyis equal to ? fzis…

A: Follow next step

Q: Find the solution of the D.E. below: 2(2x² + y*)«x – xycdy = 0 ... x* = c (4x²+y²) x* = c(x?+ 4y?) B…

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Q: Solve (x² + 4)y' = 2xy In|x] = In(y? + 4) +C O Option 1 Inlyl = In(x² + 4) +C

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Q: 4. Find the solution for the following b. y' + 2y't y = cost y) = 1, y ²) = 2

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Q: fin the general solution of (x+2y-4)dx - (2x+5-y)dy=0

A: Please see the below picture for detailed solution.

Q: se the method of variation of parameters to determine a particular solution to the given equation.…

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Q: 3 '9-x2 3+V9-a2-y? 1 dz dy x² + y² x²+y² a C = L7I Fle,0,6) dp dộ do

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Q: 3. Solve the DE ty' + 2y = ont, 4. Solve dy dr 1+ y?

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Q: 15 ven B = Find the components of -3 relative to B. 2

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Q: I. Find the value of x for which r s and its measurement. GIVEN SOLUTION Example: m23 = 3x + 3, m25…

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Q: الرابع: جد ناتج احد التكاملين التالي ين 1- Smte) xy e*y° dxdy 2- r? N4-y² ry8-x²-y" zdzdxdy x²+y2 2-…

A: 1 ∫01∫0ln(2)xyexy2dxdy first we will solve ∫0ln(2)xyexy2dx ∫0ln(2)xyexy2dx=y∫0ln(2)xexy2dxSubstitute…

Q: S (x,y.:)= 4x°y° -e°y* ++4y-x" +4y–x'6

A: It is partial derivative

Q: 4. Give the graphical significance of the constant k for the equations of the form y=(x-h)³ +k

A: Given curve is y=(x-h)3+k

Q: Choose the correct answer and show detailed and complete solution. Critical point of y = x² In x %3D…

A: To find the critical point for the given equation of y= x2 ln x

Q: (d) y = x/1 (e) y = e", y = e3, and x = 1 (f) u = 2" , y = 5", and x= 1

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Q: Find the general solution of the lines Зу + 2 y - 2 )dx + ( 2x -+ 1 )dy = 0 4 2

A: Let us consider the given differential equation f(x,y)dx+g(x,y)dy=0 Using substitution,  x=X+hy=Y+k…

Q: Solve by variable separable. 4.)(4y + yx³)dy – (2x + xy*)dx = 0 5.)2y(x +1)dy = xdx NOTE: Only the…

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Q: Find the solution of given D.E x?(1 – x)?y" + 2xy' + 4y = 0 |

A: Given:- x2(1-x)2y''+2xy'+4y=0 ⇒y''+2xx2(1-x)2y'+4x2(1-x)2y=0 Standard form…

Q: 5. Differentiate the following a) y = e*(x³ + 4) %3D b) y= x³e* 3 у %3D et c) у%3 x2

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Q: 1. Solve (D? + D;)z = 0 2. Solve (D– 2D,D, + 5D)z = 0 %3D y

A: 1) Given partial differential equation is: (Dx2+Dy2)z=0 Write auxiliary equation corresponding to…

Q: 22/ Solve two of the following D.E- dy + 4 +4y =0 A) dy B) di+2d3 - 3y=6 undetermined coeff.]

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Q: (4) (b) 10tsin(5t²- n/4)dt (4) (c) S 12(x³ + 2)ex¹+8x dx

A: We have to evaluate the integrals.

Q: 7. If y = e*², then d²y dx2 boins9 (A) (2x)(x² – 1)e*²-2 stod beniu (B) ex2 (C) 2xe*2 (D) (2 +…

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Q: 2x²+x+1 S (x− 1)(x + 1)(x − 2) dx = ₁ 11 (A) 3 (B) None 11 C 3 (D) -SA+ 1 3 E -2 B + x+1 x-2 Q dx,…

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Q: 2y4+x+ хуз dy dx a. y = x b. y = x8 – x4 C. y = Vx8 – x4 d. y %3D х — 1 e. Not in the list.

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Q: y" – 4y' + 8y = x², y(0) = 2, y'(0) = 4

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Q: What is the general solution of ху(ху5 - 1) dx + х?(1+ ху)dy3D0 ? A 2x3y5-3x² = cy? B 2x°y3 - 3x2 =…

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Q: S If 2x²+x+1 (x-1)(x + 1)(x-2) a A (B) - (D E 3 =1 3 C) None -2 B C dx = MAR √²+1 dx. dx, then the…

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Q: What value of c will satisfy y(x) = c(1 – x²) given y(0) = 1? 2 O Option 1 Option 2 3 Ontion 3…

A: Let's find.

Q: Give the general solution of: dw/dx + (4w)/x = x3

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Q: 5. Give the graphical significance of the constant a for the equations of the form y-a(x-h)²+k.

A: We have to discuss the graphical significance of given equation.

Q: (14) f (x,y)=e" (x² +y²)

A: f(x,y) = (x^2+y^2)e^-y fx= 2xe^-y fy= -(e^-y)(x^2+y^2)+ 2ye^-y fxx = 2e^-y fyy = (e^-y)(x^2+y^2)…

Q: 2) Obtain a particular solution for d*y d?y dy + +y = x³ + 2x +1 dx4

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Q: If S A 2x²+x+1 (x-1)(x+1)(x-2) 11 3 -2 11 3 None 1 E - 3 C dx = А SA + B C + 1 + = -₂2]dx x+1 + dx,…

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Q: (a) In e7 (b) eln 2 %3D (c) eln v3 %3D Preview (d) In e5

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Q: H.w Solve y'+y'-zy= -2 f yoj=Zfylcojal

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Q: 2 4 Mx(t) = -e+ 3t e' + e" + %3D 3 15

A: Given: Mxt=13et+415e3t+215e4t+415e5t

Q: For what values of m does Y = emx satisfy Y" + Y' - 2Y= 0 ?

A: For what value of m does Y=emx satisfy Y''+Y'-2Y=0

Q: 4 SS C) Jx dy

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Q: of (d) If x = ;(s2 + 12) and y = s - 12, then at the point (s, t) = (1, 1), д is equal to 0 х.

A: Given : fx , y=x2y+sin(xy)+1   x=12s2+t2      ,   y=s-t2 To find : ∂f∂t at 1 , 1

Q: 19) If y- find the value of yl.3y. 3' A) 3. C) 1 B) 0 D) 3

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Q: Determine the value of C if f(x,y) = C is the solution of (x+ 2y-3)dx+(x+2y+1)dy3D0 for x=94 and y=…

A: